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Full text of "Mathematical And Physical Papers - Iii"

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ji' ki I*!'
space in which the pendulums were swung, the resistance to the wire in the case of the spheres, the deviation of the motion of the air near the bottom of long cylindrical rods from a motion in two dimensions, in a horizontal plane, such small discrepancies as that just noticed can hardly be affirmed to be real, that is, such as would emerge from mere casual errors of observation if the above corrections were made perfectly. It is however possible that with amplitudes of vibration as large as those actually used, amounting to about 1 to start with, there may have been a very slight production of eddies, the effect of which on the time of vibration may not have been wholly insensible.
But it is not only with regard to the time of vibration that the results of Baily's experiments manifest such a remarkable agreement with theory notwithstanding the adoption of an erroneous assumption as to the relation of p to p ; the observed reduction of the arc of vibration was also found not greatly to differ from that given by calculation.
As regards the spheres, the equation (172), p. 114, gives
Now even in the case of the 1-J-irich spheres the right-hand member of this equation exceeds unity by only 0*127, so that the supposition that, in order to rectify the law connecting ^ with p, k' requires to be altered in the same ratio as k  -J does not much differ from the truth. Accordingly the calculated numbers for the spheres (p. 120) differ but little from the numbers given by observation. Calculation by aid of the table on p. 52 shows as regards the rod No. 21 that if the calculated number 287 represented the number given by observation, the assumed value (O'llG)2 of // for atmospheric density would have to be increased in the ratio of 1 to 1'400, bringing it considerably nearer to the true value as given by modern determinations. As observation gave for the logarithmic decrement 315, p! would have to be still further increased, making it somewhat too high. Similar remarks apply to the tube Nos. 35  38, which however according to Baily's figure differs much from a plain cylinder, and which moreover requires a comparatively large correction for confined space. On the whole then the pretty close agreement between theory and observation as to the decrement of arc, notwithstanding the assumption of a